MCQ
A block follows the path as shown in the figure from height $h$. If radius of circular path is $r$, then relation that holds good to complete full circle is
- A$h < 5r/2$
- B$h > 5r/2$
- C$h = 5r/2$
- ✓$h \ge 5r/2$
✓
Answer
Correct option: D.
$h \ge 5r/2$
d
(d) In order to complete a full circle, the normal force when the block is at the highest point of circular ramp should be greater than zero,
(d) In order to complete a full circle, the normal force when the block is at the highest point of circular ramp should be greater than zero,
$\mathrm{SO}$
if value of point $B=v_{B}$ Then,
At point $B, m g+N=\frac{m v_{B}^{2}}{R}$
$\mathrm{AS} N>0$
$\Rightarrow v_{B}^{2}>m g R$
At point $-A$
$\frac{m v_{A}^{2}}{2}-\frac{m v_{B}^{2}}{2}=m g(2 R)[A s \Delta K E=-\Delta P E]$
$\frac{m v_{A}^{2}}{2}=2 m g R+\frac{m v_{B}^{2}}{2}$
As $v_{B}^{2}>m g R$
$\Rightarrow \frac{m v_{A}^{2}}{2}>2 m g R+\frac{m g R}{2} \Rightarrow \frac{m v_{A}^{2}}{2}>\frac{5 m g R}{2}$
Also, $\frac{m v_{A}^{2}}{2}-0=m g h$
$\mathrm{As}, m v_{A}^{2}>5 m g R \Rightarrow m g h>\frac{5 m g R}{2}$
$\Rightarrow h>5 r/ 2$
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